Alternative Probabilistic Approach Research Articles

The Structural Reliability of the Usumacinta Bridge Using InSAR Time Series of Semi-Static Displacements

In recent years, Interferometric Synthetic Aperture Radar (InSAR) technology has been able to determine the semi-static behavior of bridges. However, most of the research about the use of InSAR in the monitoring of bridges has been applied only in deterministic assessments of their performance. Therefore, in the current manuscript, the Usumacinta Bridge, located in Mexico, was evaluated based on a probabilistic methodology to define structural reliability using images from Sentinel-1. In addition, a controlled experiment was developed using a corner reflector (CR) to evaluate the capabilities of InSAR for determining vertical displacements. In the trial, the CR was designed, oriented, and implemented, finding discrepancies concerning leveling of less than 2 mm. On the other hand, the case of the alternative probabilistic approach integrates the reliability of structures theory and probability density functions (PDFs) of displacements obtained via InSAR technology. In summary, the proposed study focused on the analysis of two years of vertical displacements and monthly velocities; then, implementing the alternative probabilistic approach, the reliability index (β) and probability of risk (PR) of the bridge were extracted, respectively. Based on the results of the experimental part of the paper, the displacements indicated maximum and minimum values of reliability index of 8.1 and 3.4, respectively. Within this context, the mean and standard deviation obtained were 5.9 and 1.4, respectively. On the other hand, the monthly velocities showed a maximum probability of risk of 2.61%, minimum value of 1.5 × 10−5%, mean of 0.4%, and standard deviation of 0.8%. Hence, the above-documented results indicate that the Usumacinta Bridge did not suffer any damage during its overloading condition period.

Optimal inference of molecular interaction dynamics in FRET microscopy

Intensity-based time-lapse fluorescence resonance energy transfer (FRET) microscopy has been a major tool for investigating cellular processes, converting otherwise unobservable molecular interactions into fluorescence time series. However, inferring the molecular interaction dynamics from the observables remains a challenging inverse problem, particularly when measurement noise and photobleaching are nonnegligible-a common situation in single-cell analysis. The conventional approach is to process the time-series data algebraically, but such methods inevitably accumulate the measurement noise and reduce the signal-to-noise ratio (SNR), limiting the scope of FRET microscopy. Here, we introduce an alternative probabilistic approach, B-FRET, generally applicable to standard 3-cube FRET-imaging data. Based on Bayesian filtering theory, B-FRET implements a statistically optimal way to infer molecular interactions and thus drastically improves the SNR. We validate B-FRET using simulated data and then apply it to real data, including the notoriously noisy invivo FRET time series from individual bacterial cells to reveal signaling dynamics otherwise hidden in the noise.

An Alternative Probabilistic Approach for Reliability Assessment of Rotorcraft Structures

An alternative probabilistic approach is proposed to assess the reliability of rotorcraft structures. According to the approach, safe boundaries of reliability predictions (i. e., conservative ones with additional safety margins) are calculated instead of exact values of the reliability as usually estimated in conventional analysis. Due to additional safety margins, these boundaries are suggested for practical engineering applications. The proposed approach is based on two main ideas, namely (a) prediction of a relatively small population of independent coarse estimations of reliability and (b) application of sampling methods to predict reliability for each individual coarse estimation. Robustness and convenience of the developed approach and its computational implementation are demonstrated for four scenarios considering two problems (simplified analytical and realistic finite element analysis–based ones) under two sets of input data providing the probability of failure (POF) close to 1e-6 and 1e-9, respectively. High accuracy of predictions according to the developed approach is independently verified by comparison with known "exact" references: closed-form solutions for the analytical problem and by direct Monte Carlo simulation for the numerical one. The proposed approach can be recommended as an efficient practical solution for a broad range of reliability assessments of rotorcraft structures requiring both (i) low POF (e. g., below 1e– 6) and (ii) relatively complex time-consuming structural definitions (e. g., compute times in hours for each quasi-deterministic simulation).

Revision of path-integral approach to radiative transfer

During the last decades, a number of publications have appeared, which dealt with applications of path-integral methods in modeling of radiative/light transfer through various turbid media. This approach seems to be an elegant way how to incorporate multiple scattering effects into calculations of radiometric quantities and thus provides an alternative to time-consuming numerical simulations or to too simplifying approximations. However, some of the published works are based on incorrect mathematical assumptions and the functions derived there actually yield infinite value results in particular calculations. They appear to be unusable without some additional ad hoc normalization. It is therefore questionable, how plausible the conclusions drawn in those works are. This paper revises the derivations of a path-integral form of the Green’s function in radiative transfer problems, reveals their critical points, and compares the resulting formulas with the formulas obtained by an alternative probabilistic approach. Moreover, it provides at least an approximate expressions usable for radiance calculations in turbid media.

Another probabilistic construction of Φ22n

This note provides an alternative probabilistic approach to the Φ2n theory in dimension 2. The key idea is to study the concentration phenomenon of martingales associated to polynomials of Gaussian variables. This is based on an adaptation of the work of Lacoin-Rhodes-Vargas [3] on the quantum Mabuchi K-energy.

Implementation of PPP-GNSS measurement technology in the probabilistic SHM of bridge structures

The use of geodetic-grade GNSS (Global Navigation Satellite System) receivers is increasingly evolving in the Structural Health Monitoring (SHM) of infrastructure. In this sense, the Precise Point Positioning GNSS (PPP-GNSS) is becoming very popular since it requires only one GNSS receiver. This paper presents a novel SHM technique by integrating the PPP-GNSS measurement technology and an alternative probabilistic approach. Such an approach is based on the study of the stochastic behavior of displacements and their corresponding probability density functions. As a case of study, the El Carrizo Bridge is studied. Results validate the accuracy of the PPP-GNSS measurement technology, and the potential benefits of the alternative probabilistic SHM approach since risk can be extracted using a single GNSS receiver in terms of reliability index and probability of failure. Finally, based on the probabilistic evaluation, it is demonstrated that the El Carrizo Bridge presents an adequate behavior after its rehabilitation.

Gaussian processes with logistic mean function for modeling wind turbine power curves

The wind turbine power curve (WTPC) is a mathematical model built to capture the input-output relationship between the generated electrical power and the wind speed. An adequately fitted WTPC aids in wind energy assessment and prediction since the actual power curve will differ from that provided by the manufacturer due to a variety of reasons, such as the topography of the wind farm, equipment aging, and multiple system faults. As such, this paper introduces a novel approach for WTPC modeling that combines Gaussian process (GP) regression, a class of probabilistic kernel-based machine learning models, and standard logistic functions. This semi-parametric approach follows a Bayesian reasoning, in the sense of maximizing the marginal likelihood to learn the parameters and hyperparameters through a variational sparse approximation to the GP model. Using real-world operational data, the proposed approach is compared with the state-of-the-art in WTPC modeling and with an alternative probabilistic approach based on generalized linear models and logistic functions. Finally, we evaluate the proposed model in its extrapolation ability for unmodelled data.

Partitioning heterozygosity in subdivided populations: Some misuses of Nei's decomposition and an alternative probabilistic approach.

Nei's decomposition of total expected heterozygosity in subdivided populations into within- and between-subpopulation components, HS and DST , respectively, is a classical tool in the conservation and management of genetic resources. Reviewing why this is not a decomposition into independent terms of within- and between-subpopulation gene diversity, we illustrate how this approach can be misleading because it overemphasizes the within-subpopulation component compared to Jost's nonadditive decomposition based on gene diversity indices. Using probabilistic partitioning of the total expected heterozygosity into independent within- and between-subpopulation contributions, we show that the contribution of the within-subpopulation expected heterozygosity to the total expected heterozygosity is not HS , as suggested by Nei's decomposition, but HS /s, with s being the number of subpopulations. Finally, we compare three possible approaches of decomposing total heterozygosity in subdivided populations (i.e., Nei's decomposition, Jost's approach, and probabilistic partitioning) with regard to independence between terms and sensitivity to unequal subpopulation sizes. For the conservation and management of genetic resources, we recommend using probabilistic partitioning and Jost's differentiation parameter rather than Nei's decomposition.

Evaluating the interference from fixed wireless access TDMA systems into HAPS systems: a probabilistic approach

This study presents a probabilistic model to assess the co-channel interference produced by multiple transmitters of a fixed wireless access network into a high altitude platform stations (HAPS) victim receiver. The authors propose an alternative probabilistic approach that avoids the worst case assumptions usually considered in traditional interference calculation methods, by considering the random modelling of some of the technical parameters involved. More specifically, the geographic positions of fixed wireless access system transmitters are modelled by a two-dimensional point process and their antenna gains in the sidelobe region are modelled as gamma distributed random variables. The proposed method is validated by comparing the minimal operating distance resulting from the traditional deterministic interference calculation methods and that obtained with th proposed approach. Results corresponding to the four possible interfering scenarios indicate that the proposed probabilistic approach leads to a reduction in coordination distances.

Ship Seakeeping Operability, Motion Control, and Autonomy - A Bayesian Perspective

Ship seakeeping operability refers to the quantification of motion performance in waves relative to mission requirements. This is used to make decisions about preferred vessel designs, but it can also be used as comprehensive assessment of the benefits of ship-motion-control systems. Traditionally, operability computation aggregates statistics of motion computed over over the envelope of likely environmental conditions in order to determine a coefficient in the range from 0 to 1 called operability. When used for assessment of motion-control systems, the increase of operability is taken as the key performance indicator. The operability coefficient is often given the interpretation of the percentage of time operable. This paper considers an alternative probabilistic approach to this traditional computation of operability. It characterises operability not as a number to which a frequency interpretation is attached, but as a hypothesis that a vessel will attain the desired performance in one mission considering the envelope of likely operational conditions. This enables the use of Bayesian theory to compute the probability of that this hypothesis is true conditional on data from simulations. Thus, the metric considered is the probability of operability. This formulation not only adheres to recent developments in reliability and risk analysis, but also allows incorporating into the analysis more accurate descriptions of ship-motion-control systems since the analysis is not limited to linear ship responses in the frequency domain. The paper also discusses an extension of the approach to the case of assessment of increased levels of autonomy for unmanned marine craft.

Brief communication: A probabilistic approach to age estimation from infracranial sequences of maturation

Infracranial sequences of maturation are commonly used to estimate the age at death of nonadult specimens found in archaeological, paleoanthropological, or forensic contexts. Typically, an age assessment is made by comparing the degree of long-bone epiphyseal fusion in the target specimen to the age ranges for different stages of fusion in a reference skeletal collection. While useful as a first approximation, this approach has a number of shortcomings, including the potential for "age mimicry," being highly dependent on the sample size of the reference sample and outliers, not using the entire fusion distribution, and lacking a straightforward quantitative way of combining age estimates from multiple sites of fusion. Here we present an alternative probabilistic approach based on data collected on 137 individuals, ranging in age from 7- to 29-years old, from a documented skeletal collection from Coimbra, Portugal. We then use cross validation to evaluate the accuracy of age estimation from epiphyseal fusion. While point estimates of age can, at least in some circumstances, be both accurate and precise based on the entire skeleton, or many sites of fusion, there will often be substantial error in these estimates when they derive from one or only a few sites. Because a probabilistic approach to age estimation from epiphyseal fusion is computationally intensive, we make available a series of spreadsheets or computer programs that implement the approach presented here.

Moments of Discounted Dividends for a Threshold Strategy in the Compound Poisson Risk Model

We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.

Probabilistic Approach for Design and Hydrologic Performance Assessment of Reconstructed Watersheds

The oil sands mining industry in Canada has made a commitment to reclaim mining areas to an equivalent capability to that which existed prior to mining. An essential requirement in the design of reclamation covers to meet this objective is that all covers must have a sufficient available water holding capacity (AWHC) in order to supply sufficient moisture for vegetation over the summer moisture deficit typical in the region. AWHC is currently based on static evaluations of wilting point and field capacity under a constant annual evapotranspiration demand. This paper presents an alternative probabilistic approach by which the hydrologic performance of these reclamation soil covers can be assessed. A field-calibrated water balance model is used along with the available historical meteorological record to estimate the maximum soil moisture deficit that a soil cover is able to sustain over the growing season. Frequency curves of the maximum annual moisture deficit are used to assess the probability that a cover is able to provide any particular threshold of moisture demand. The method also allows for a quantification of the predictive uncertainty of the model. The predictive uncertainty is used as a margin of safety to estimate a design value of moisture deficit for various alternative cover designs. This paper recommends procedures for a frequency-based assessment and design of reclamation soil covers in the oil sands industry. This method takes into account climatic variability as well as parameter uncertainty in estimating the soil moisture deficit.

Deterministic and probabilistic approaches to the development of pH total maximum daily loads: a comparative analysis

The most commonly used deterministic approach to the development of total maximum daily loads (TMDLs) fails to explicitly address issues related to a margin of safety and inherent variability of streamflows in the process of TMDL development. In this paper, the deterministic approach to pH TMDL development for Beech Creek watershed, Muhlenberg County, Kentucky, proposed by Ormsbee, Elshorbagy and Zechman is discussed. The shortcomings and the limitations of the assumptions associated with the deterministic approach are highlighted. An alternative probabilistic approach, to cope with the percentile-based water quality standards based on Monte Carlo simulation, is presented and compared to the deterministic approach. The proposed probabilistic approach provides a deeper insight into the issue of uncertainty and emphasizes the importance of handling the water quality standards and TMDLs in terms of magnitude and frequency rather than a single-valued approach. Expected exceedances and the confidence of compliance with percentile-based standards are estimated. Accordingly, an objective method of estimating the margin of safety for pH TMDLs is proposed.